I have a drawing with a lot of rectangles adjacent to each other which I have filled with a solid fill. I now found out that one of the rectangles is wrong. So I want to delete it. When I click on the border of that rectangle, there appears to be selected only a line (or all 4 border lines of the rectangle), and pressin del does not have any (visible) effect. When I click into the rectangle, all corners within the drawing are selected. I absolutely have no idea how to select the wrong rectangle alone to get rid of it.

It sounds like you have created a single solid fill over all rectangles. In this case, the solid fill is one entity and you cannot remove an individual part (loop) from it. You might want to create an individual solid fill for each rectangle instead to be more flexible.